Hyperparameter and Kernel Learning for Graph Based Semi-Supervised Classification

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1、HyperparameterandKernelLearningforGraphBasedSemi-SupervisedClassificationAshishKapoory,Yuan(Alan)Qiz,HyungilAhnyandRosalindW.PicardyyMITMediaLaboratory,Cambridge,MA02139fkapoor,hiahn,picardg@media.mit.eduzMITCSAIL,Cambridge,MA02139alanqi@csail.mit.eduAbstractTherehavebeenmanygraph-basedapproa

2、chesforsemi-supervisedclas-sification.Oneproblemisthatofhyperparameterlearning:performancedependsgreatlyonthehyperparametersofthesimilaritygraph,trans-formationofthegraphLaplacianandthenoisemodel.WepresentaBayesianframeworkforlearninghyperparametersforgraph-basedsemi-supervisedclassification.G

3、ivensomelabeleddata,whichcancontaininaccuratelabels,weposethesemi-supervisedclassificationasanin-ferenceproblemovertheunknownlabels.ExpectationPropagationisusedforapproximateinferenceandthemeanoftheposteriorisusedforclassification.ThehyperparametersarelearnedusingEMforevidencemaximization.Weal

4、soshowthattheposteriormeancanbewrittenintermsofthekernelmatrix,providingaBayesianclassifiertoclassifynewpoints.Testsonsyntheticandrealdatasetsshowcaseswheretherearesignificantimprovementsinperformanceovertheexistingapproaches.1IntroductionAlotofrecentworkonsemi-supervisedlearningisbasedonregul

5、arizationongraphs[5].Thebasicideaistofirstcreateagraphwiththelabeledandunlabeleddatapointsastheverticesandwiththeedgeweightsencodingthesimilaritybetweenthedatapoints.Theaimisthentoobtainalabelingoftheverticesthatisbothsmoothoverthegraphandcompatiblewiththelabeleddata.Theperformanceofmostofthe

6、sealgorithmsdependsupontheedgeweightsofthegraph.OftenthesmoothnessconstraintsonthelabelsareimposedusingatransformationofthegraphLaplacianandtheparametersofthetransformationaffecttheperformance.Further,theremightbeotherparametersinthemodel,suchasparameterstoaddresslabelnoiseinthedata.Findinga

7、rightsetofparametersisachallenge,andusuallythemethodofchoiceiscross-validation,whichcanbeprohibitivelyexpensiveforreal-worldproblemsandproblematicwhenwehavefewlabeleddatapoints.Mostofthemethodsignoretheproblemoflearninghyperparametersthatdeterminet